System and method for relativistic statistical securities trading

ABSTRACT

A system comprising a processor configured to calculate a location for a server along a communication link between a first trading center and a second trading center based at least in part on a property of the communication link. The server may be configured to send first trade instructions for trading a first financial instrument to the first trading center and send second trade instructions for trading a second financial instrument to the second trading center.

RELATED APPLICATIONS

The present application claims the benefit under 35 U.S.C. §119(e) ofU.S. Provisional Application Ser. No. 61/349,238, filed May 28, 2010,entitled “SYSTEM AND METHOD FOR RELATIVISTIC STATISTICAL SECURITIESTRADING,” which is incorporated herein by reference in its entirety.

BACKGROUND

Financial markets allow for the buying and selling of a broad variety offinancial instruments including stocks, bonds, and commodities. In somemarkets, financial instruments can be traded electronically by usingcomputer technology. The speed at which such computer technology canoperate, enables high-frequency (electronic) trading—the trading offinancial instruments multiple times in a short time period.High-frequency trading is widespread. Indeed, by some estimates,high-frequency trading accounts for over seventy percent of equitytrades in the United States.

Today, high-frequency trading platforms and algorithms are used to tradefinancial instruments at such high speeds, that latencies between atrading order (e.g., “buy 300 shares of stock A”) and a response to thetrading order (e.g., “order has been filled”) are often below 500microseconds. Accordingly, high-frequency traders are able to takeadvantage of opportunities occurring at microsecond level rather thanconventional “long-term” investing at time scales of months or years.

High-frequency traders compete with one another to take advantage ofshort-term market opportunities on the basis of how fast the traders canexecute high-frequency trades. The faster a high-frequency trader cantrade, the more he is able to take advantage of available opportunities.The speed of high-frequency trading depends on computers, networks, andsoftware used to implement it.

SUMMARY

Accordingly, in some embodiments a system for calculating a serverlocation may be provided. The system may comprise a processor configuredto calculate a location for a server along a communication link betweena first trading center and a second trading center based at least inpart on a property of the communication link.

In some embodiments, a method for calculating a server location may beprovided. The method may comprise calculating, with a processor, alocation for a server along a communication link between a first tradingcenter and a second trading center based at least in part on a propertyof the communication link.

In some embodiments, a computer-readable storage medium may be provided.The computer-readable storage medium may be encoded withprocessor-executable instructions that, when executed by a processor,cause the processor to perform a method comprising calculating, with aprocessor, a location for a server along a communication link between afirst trading center and a second trading center based at least in parton a property of the communication link.

In some embodiments, a system for selecting one or more trading centersmay be provided. The system may comprise a server configured to select afirst trading center from a plurality of trading centers based at leastin part on a characteristic of a first financial instrument traded atthe first trading center and a property of a communication link betweenthe first trading center and a second trading center in the plurality oftrading centers.

In some embodiments, a method for selecting one or more trading centersmay be provided. The method may comprise selecting, with a server at apredetermined location, a first trading center from a plurality oftrading centers based at least in part on a characteristic of a firstfinancial instrument traded at the first trading center and a propertyof a communication link between the first trading center and a secondtrading center in the plurality of trading centers.

In some embodiments, a computer-readable storage medium may be provided.The computer-readable storage medium may be encoded withprocessor-executable instructions that, when executed by a processor,cause the processor to perform a method comprising selecting, with aserver at a predetermined location, a first trading center from aplurality of trading centers based at least in part on a characteristicof a first financial instrument traded at the first trading center and aproperty of a communication link between the first trading center and asecond trading center in the plurality of trading centers.

BRIEF DESCRIPTION OF DRAWINGS

The accompanying drawings are not intended to be drawn to scale. In thedrawings, each identical or nearly identical component that isillustrated in various figures is represented by a like numeral. Forpurposes of clarity, not every component may be labeled in everydrawing. In the drawings:

FIG. 1 is a block diagram of an exemplary operating environment for asystem in accordance with some embodiments of the present disclosure.

FIGS. 2 a and 2 b are block diagrams illustrating a trading center and aserver in accordance with some embodiments of the present disclosure.

FIG. 3 is a block diagram of another exemplary operating environment fora system in accordance with some embodiments of the present disclosure.

FIG. 4 is an illustrative space-time diagram of an exemplary distributedfinancial transaction executed using methods known in the prior art.

FIG. 5 is an illustrative space-time diagram of an exemplary distributedfinancial transaction executed in accordance with some embodiments ofthe present disclosure.

FIG. 6 is a flowchart of an illustrative process for executing adistributed financial transaction in accordance with some embodiments ofthe present disclosure.

FIG. 7 is a flowchart of an illustrative process for calculating alocation for a server in accordance with some embodiments of the presentdisclosure.

FIG. 8 is a flowchart of an illustrative process for selecting tradingcenters to execute a distributed financial transaction in accordancewith some embodiments of the present disclosure.

FIG. 9 is a block diagram generally illustrating an example of acomputer system that may be used in implementing aspects of the presentdisclosure.

DETAILED DESCRIPTION

The inventors have recognized that the success of a high-frequencytrading (HFT) strategy depends on the speed at which financialtransactions are executed and that this speed depends on the amount oftime it takes for information to propagate through the computerinfrastructure (e.g., computers, databases, networks, etc.) used toimplement the high-frequency trading strategy. The inventors haveappreciated that information propagation latencies lead to delays thatmay limit the effectiveness of HFT strategies because these delays maylimit how quickly HFT systems may trade.

The inventors have recognized and appreciated that delays due toinformation propagation latencies are more pronounced when portions ofthe computer infrastructure are not located in one place. In this case,the amount of time it takes for information to propagate through thecomputer infrastructure may be greater than in the case when all thecomputer infrastructure is co-located. For instance, the latency betweenthe time a computer in one location (e.g., London) sends a buy order toa trading center in a second location (e.g., New York) and the time thecomputer receives a response to the order from the trading center maydepend on the amount of time it takes for the order information and forthe response to travel between these locations.

It should be appreciated that trades in conventional HFT systems mayoccur on the micro-second scale, whereas 67 milliseconds (several ordersof magnitude higher) are required for light to travel between antipodalpoints along the Earth's surface. Thus, the amount of time forinformation to travel between two geographically-separated locations mayimpact how quickly trading, distributed across geographically-separatelocations, can take place.

Though such disparity is especially pronounced for HFT strategies thatutilize geographically-separated computer infrastructure, informationpropagation delays are relevant across much shorter distances (e.g.,even a single city block).

The inventors have further recognized and appreciated that informationpropagation latencies may limit the speed at which high-frequencystrategies for distributed trading may operate. Consider a distributedhigh-frequency strategy that involves selling one security at a tradingcenter in London (e.g., London stock exchange) and simultaneously buyinganother security at a trading center in New York (e.g., NASDAQ).Conventional approaches to implementing such a distributed andcoordinated trading strategy comprise using a server co-located with oneof the two trading centers to execute the strategy—the computer placesorders to each of the trading centers and receives responses from thetrading centers. Accordingly, these conventional approaches are limitedby the amount of time it takes for information to propagate along acommunication link between the two trading centers.

The inventors have recognized and appreciated that it may beadvantageous to control the placement of the server used to execute acoordinated trading strategy in order to reduce the latency ofinformation propagation. Controlling the placement of the server mayaddress some of the shortcomings of the above-described conventionalapproaches for implementing distributed high-frequency strategies.However, not every embodiment addresses every one of these drawbacks,and some embodiments may not address any of them. As such, it should beappreciated that the invention is not limited to addressing all or anyof the above-discussed drawbacks of these conventional approaches.

Placing a server at a location along a communication link between twotrading centers in a way that reduces the latencies of informationpropagation during a distributed trade may allow such trades to occurmore frequently and may allow high-frequency distributed trading tooccur at a higher speed than using a conventional approach in which aserver is co-located with one of the trading centers. As described ingreater detail below, the suitability of a location to place the servermay be evaluated based on the nature of the distributed trade (e.g.,characteristics of the financial instruments traded) and/or a propertyof the communication link between the two trading centers (e.g., thelatency of information propagation along the link).

The inventors have further appreciated that it may not be possible toplace a server used to execute coordinated trades at some locationsalong a communication link between two trading centers. For instance, iftrading centers in New York and London were connected by a trans-oceanicfiber-optic cable, it may be prohibitively expensive or impractical toplace the server at a location in the ocean, if such a location weredetermined to be the most suitable location to place the server.

The inventors have further recognized that if the location of the serverused to execute distributed trades were fixed, then the trading centersused to execute the coordinated trade may be selected in a way thatreduces the latencies of information propagation during the trade. Forinstance, if it were possible to execute a coordinated trade usingtrading centers in New York and London or trading centers in Hong Kongand Chicago, then the server may select one of these pairs to executethe coordinated trade. As described in greater detail below, thisselection may be informed by the nature of the coordinated trade (e.g.,characteristics of the financial instruments traded), the location ofthe server used to execute the trading, and a property of thecommunication link between the two trading centers.

A block diagram of an illustrative system 100 comprising a server 106for controlling the execution of a distributed trade is shown in FIG. 1.Server 106 may be configured to control execution of a distributed tradeby sending one set of trade instructions to trading center 102 andanother set of trade instructions to trading center 110. The tradingcenters may execute trades in response to the instructions received fromthe server 106 and may send information confirming the execution of thetrades back to server 106. Alternatively, one or both of the tradingcenters may not execute a trade and may send confirmation to server 106indicating the trade was not performed.

Server 106 may be embodied in any of numerous forms, such as arack-mounted computer, a desktop computer, a laptop computer, or atablet computer. Additionally, server 106 may be embodied in a devicenot generally regarded as a computer, but with suitable processingcapabilities, including a Personal Digital Assistant (PDA), a smartphone or any other suitable portable or fixed electronic device.Additionally, server 106 may be embodied as a network switch capable ofoperating at one or more network layer (i.e., any layer of the OpenSystems Interconnection Model).

Trading center 102 and trading center 110 may provide facilities and/orservices for traders to trade financial instruments. Trading centers mayallow human traders to trade financial instruments and/or may allowtrades to be entered electronically by a computer. Trading centers maycomprise one or more computers and one or more networks connecting thesecomputers. A trading center may be any of numerous types of tradingcenters such as a financial exchange (e.g., New York Stock Exchange,NASDAQ, London Stock Exchange, etc.) or an over-the-counter market.

Each trading center may receive trade instructions comprising orderinformation, process the received instructions, and send out responsesto the received trade instructions.

Trading center 102 and trading center 110 may be communicatively coupledby communication link 104. Communication link 104 may be any suitablecommunication link and may be realized using any of numeroustechnologies. In some embodiments, communication link 104 may be a wiredlink and may comprise a transmission line designed to carryelectromagnetic waves. The transmission line may be any suitable type oftransmission line and may be a ladder line, coaxial cable, a fiber opticcable, and/or a waveguide. In some embodiments, the communication linkmay comprise a single type of wired connection (e.g., the link mayconsist only fiber optic cable), while in other embodiments differenttypes of transmission lines may be used together. Additionally, thecommunication link may comprise any hardware necessary for facilitatinginformation transport across the link over any suitable distance. Forinstance, the communication link may comprise one or more repeaters.

In some embodiments, communication link 104 may be a wireless linkimplemented using any suitable wireless technology to facilitateinformation transport without use of wires. Communication link 104 maytransmit information using electromagnetic waves of any suitablefrequency. For example, frequencies in the radio, microwave, visible,infrared, and ultra-violet ranges of the electromagnetic spectrum may beused. Communication link 104 may comprise any wireless technology fortransmitting information including satellites, transmitters, receivers,antennas, repeaters, and/or radios. Still in other embodiments,communication link 104 may comprise both wired and wirelesscommunication links. For instance, one segment of the communication linkmay be fiber-optic cable and another segment of the communication linkmay be realized using radio-frequency communications equipment.

Server 106 may be operatively coupled to communication link 104 atlocation 108. Location 108 may be a location at which or near which theserver is operatively coupled to communication link 104 may be alocation chosen to reduce the latency executing a distributed trade byreducing the latency of information propagation during the trade. Itshould be appreciated that the latency of information propagation fromserver 100 to trading center 102 may depend on the location 108. The wayin which location 108 is chosen is described in greater detail belowwith reference to FIG. 7.

Accordingly, server 106 may send information to and receive informationfrom trading centers 102 and 110 by using communication link 104.Communication link 104 may transport information from server 106 atlocation 108 to the location of trading center 102 or the location oftrading center 104. In this way, server 106 may use communication link104 to send trade instructions to trading center 102 and trading center110 as well as receive confirmations of completed trades from thesetrading centers.

Trade instructions sent from server 106 to either one of the tradingcenters may be any instructions indicating one or more orders to beexecuted at the trading center. Each order many be any of numerous typesof orders and may be an order corresponding to one or more financialinstruments traded at the trading center. An order may be an order tobuy and/or to sell one or more financial instruments. An order may be amarket order (buy/sell at the current market price) or a limit order(buy/sell only at a certain price). Though, trade instructions may beany instructions for any order that a trading center is able to process,as the invention is not limited in this respect.

Trade instructions sent from server 106 to trading center 102 may bedifferent than the trade instructions sent from server 106 to tradingcenter 110. For instance, trade instructions sent to trading center 102may be instructions to buy an amount (e.g., number of shares) of onefinancial instrument, whereas trade instructions sent to trading center110 may be instructions to sell an amount of another financialinstrument.

Trade instructions sent to trading center 102 and trading center 110 mayspecify any of numerous trading strategies. For example, theinstructions may specify a statistical arbitrage trade such as a pairstrade. A pairs trade may comprise betting on a temporary variation inprices of two related (e.g., correlated and/or cointegrated) financialinstruments. For instance, a pairs trade may comprise betting that theprice of one financial instrument may increase and the price of anotherfinancial instrument may decrease. Pairs trading may be accomplished byappropriately selling and buying these financial instruments as is knownin the art. A pairs trade may also comprise betting on other aspects ofthe behavior of financial instruments such as volatility. Though, theinstructions may specify other statistical arbitrage strategies that areknown in the art such as multi-factor statistical arbitrage andvolatility arbitrage. Still other distributed trading strategies, notonly those related to statistical arbitrage, may be used as theinvention is not limited in this respect.

Trade instructions may comprise orders for buying and selling one ormore financial instruments. A financial instrument may be any ofnumerous financial instruments. For instance, a financial instrument maybe an equity, a fixed-income product, a currency, a depository receipt,a derivative, and/or a foreign-exchange instrument. An equity may be anysuitable equity and may be a stock. A fixed income product may be anysuitable fixed income product such as deposits, Treasury bills,commercial paper, a certificate of deposit, a bond (of any type), and anannuity. A derivative may be any suitable derivative contract includingoptions, futures, forwards, swaps, and repurchase agreements. Though,the above list of financial instruments is not an exhaustive list offinancial instruments and any financial instrument, for which an ordermay be processed at a trading center, may be used.

Financial instruments may be traded at one or multiple trading centers.For instance, they may be “cross-listed” at multiple exchanges. In theillustrative example of FIG. 1, a financial instrument may be tradedboth at trading center 102 and at trading center 110. As such server 106may send trade instructions to trade that financial instrument at eitherone or both of the trading centers.

Server 106 may be configured to control the execution of any suitabletrading strategy. In some embodiments, server 106 may be configured tocontrol the execution of a trading strategy by a human user. In theillustrative example of FIG. 1, server 106 may be configured by user112. User 112 may configure server 106 remotely by using computer 114,which may be connected to server 106 via network 116. Network 116 maycomprise, for example, the Internet, a LAN, a WAN and/or any other wiredor wireless network, or combination thereof. Computer 114 and server 106may communicate through any suitable networking protocol because themanner in which information is transferred between computer 114 andserver device 106 is not a limitation of the present invention.

Illustrative system 100 may be implemented in any number of ways. Forinstance, though not depicted in FIG. 1, system 100 may comprise anysuitable number of trading centers (i.e., more than two trading centers)and server 106 for controlling execution of a trading strategy may beconfigured to send trade instructions to and receive information fromany of the trading centers. Also, trading center 102, trading center110, server 106, and computer 106 may comprise a computer or a pluralityof computers, as the invention is not limited in this respect.

FIGS. 2 a and 2 b show illustrative block diagrams of softwarecomponents that may execute at a trading center (e.g., trading center102) and server 106 to perform or help to perform functions describedwith reference to FIG. 1. FIG. 2 a. shows an illustrative block diagramof software components of an electronic trading center 210. In theembodiment illustrated, the software components may be stored ascomputer-executable instructions and configuration parameters in amemory coupled to trading center 210.

In the illustrated embodiment, trading center 210 includes an ordercommunication module 212. Components within the order communicationmodule may perform functions related to receiving trade instructions andsending out responses to received trade instructions. For instance,components within the order communication module 212 may receive tradeinstructions indicating an order to buy a financial instrument and/or tosell a financial instrument. Components within the order communicationmodule 212 may send out a response to the trade instructions indicating,for example, whether or not the order was filled. It should beappreciated that order communication module 212 may receive anyinstructions for any type of order that may be executed by tradingcenter 210.

Trading center 210 may also comprise order processing module 214.Components within module 214 may be used to execute orders received byorder communication module 212, and they may execute orders in anysuitable way as known in the art. For instance, components within module214 may maintain an electronic order queue to keep track of the tradeinstructions and the order (i.e., time sequence) in which they arrived.Components within module 214 may execute some orders and may not executeother orders depending on market conditions.

It should be recognized that the software components illustrated in FIG.2 a are merely illustrative and that trading center 210 may beimplemented in any other suitable way. It may have additionalfunctionality not described in the example of FIG. 2 a and anyfunctionality that was described in reference to FIG. 2 a may beimplemented differently, as the invention is not limited in thisrespect. Finally, any of the software modules described with referenceto FIG. 2 a may be alternatively be implemented in hardware or using acombination of software and hardware.

FIG. 2 b shows an illustrative block diagram of software components thatmay execute within server 220. In the illustrated embodiment, softwarecomponents may be stored as computer-executable instructions andconfiguration parameters in computer-readable storage media associatedwith server 220. Components within the trading control module 222 mayperform functions related to executing a distributed trading strategycomprising the trading of one or more securities at multiple tradingcenters. Accordingly, components within module 222 may control theexecution of a trade distributed across multiple trading centers.

Components within module 222 may determine a time at which a tradeshould be made and what the trade should be. The components maydetermine which financial instruments should be traded as part of attrade, amounts of each instrument that should be traded (e.g., number ofshares of a stock), and the manner in which they should be traded (e.g.,bought or sold) traded in a trade. Accordingly, the components of module222 may be used to specify trade instructions for the trade. Further,components within module 222 may be used to determine whether tradeconditions—criteria for making trades—have been met.

Server 220 may comprise an order communication module 226. Components oforder communication module 226 may perform functions related to sendingtrade instructions to one or more trading centers and receivingresponses to the trade instructions, or any other communications, fromthe one or more trading centers. For instance, components within theorder communication module 224 may send trade instructions indicating anorder to buy a financial instrument and/or to sell a financialinstrument. Components within the order communication module 224 mayreceive a response to the trade instructions indicating, for example,whether or not the order was filled.

Server 220 may comprise a network configuration module 226. Componentswithin network communication module 226 may be used to configure server220 to communication with one or more trading centers (e.g., first andsecond trading centers described with reference to FIG. 1) and mayconfigure server 220 to communicate with the trading centers along aspecific communication link. In addition, components in networkcommunication module 226 may allow for server 220 to be configuredremotely. For instance, they may allow for server 220 to be configuredremotely by user 112 as described with reference to FIG. 1.

It should be recognized that the software components illustrated in FIG.2 b are merely illustrative and that server 220 may be implemented inany other suitable way. Server 220 may have additional functionality notdescribed in the example of FIG. 2 b and any functionality that wasdescribed in reference to FIG. 2 a may be implemented differently, asthe invention is not limited in this respect. Finally, any of thesoftware modules described with reference to FIG. 2 b may bealternatively implemented in hardware or using a combination of softwareand hardware.

Recall that if the location of a server (e.g., server 106) used toexecute a distributed and coordinate trading with multiple tradingcenters were fixed, then the trading centers used to execute thecoordinated trade may be selected in a way that reduces the latencies ofinformation propagation during the trade. A system operating inaccordance with this observation is illustrated in FIG. 3.

FIG. 3 shows a block diagram of an illustrative system 300 comprising aserver 306 for controlling the execution of a distributed trade. In theillustrative system 300, server 306 is communicatively coupled, at (ornear) location 316, to communication link 312 between trading center 302and trading center 310. Server 306 is also communicatively coupled, at(or near) location 318, to communication link 314 between trading center304 and trading center 308.

Server 306 may be configured to select one or more trading centers.Server 306 may control execution of a distributed and coordinated tradeon the selected trading centers. Server 306 may select a pair of tradingcenters to which it is connected. The pair of trading centers may becommunicatively coupled by a communication link. In the illustrativeexample of FIG. 3, server 306 may select the trading centers 302 and 310or may select the trading centers 305 and 308 to execute a trade.

Server 306 may select one or more trading centers to execute a trade inany of numerous ways. The selection may depend on the location at whichor near which server 306 is coupled to a communication link between oneof the selected trading centers and another trading center. Theselection may depend at least in part on a characteristic of one or morefinancial instruments traded at one of the trading centers. When atleast two trading centers are selected, the selection may also depend ona property of the communication link between the two trading centers.The way in which the trading centers are chose is described in greaterdetail below with reference to FIG. 8.

Server 306 may be embodied in any of numerous forms and may be embodiedin one of the forms that server 106 may be embodied in, as describedwith reference to FIG. 1. For instance, server 306 may be a PDA, adesktop computer, and a network switch. Though may other embodiments ofserver 306 are possible as the invention is not limited in this respect.

Server 306 may control a distributed trade in a pair of trading centers.To this end, server 306 may be configured to send one set of tradeinstructions to one trading center in a pair of trading centers andanother set of trade instructions to another trading center in the pair.For example, server 306 may send one set of trade instructions tradingcenter 302 (or 304) and another set of trade instructions to tradingcenter 310 (or 308). As is the case with system 100, the trading centersmay execute trades in response to the instructions received from theserver 306 and may send information confirming the execution of thetrades back to server 306. Alternatively, one or both of the tradingcenters may not execute a trade and may send confirmation to server 306indicating the trade was not performed.

In system 300, communication links 312 and 314 may be any suitablecommunication links and may be communication links of the type describedwith reference to FIG. 1. Similarly, trading centers and tradeinstructions may be any suitable trading centers and trade instructionsand may be trading centers and trade instructions of the type describedwith reference to FIG. 1.

Server 306 may be configured to control the execution of any suitabletrading strategy. It may be configured automatically by a computer ormanually by a human user. For instance, server 306 may be configured byuser 326. User 326 may configure server 306 remotely by using computer324 connected to server 306 via network 320.

It should be appreciated that many variations of illustrative system 300are possible. For instance, though not depicted in FIG. 3, system 300may comprising any suitable number of trading centers and server 306 maybe configured to select one or more trading centers from among anynumber of trading centers (not just four as illustrated in FIG. 3). Eachtrading center, server and computer shown in FIG. 3 may comprise acomputer or a plurality of computers, as the invention is not limited inthis respect.

In the illustrative systems 100 and 300, described with respect to FIGS.1 and 3, servers 106 and 306 may not be co-located with the tradingcenters and, instead, may be located at intermediate locations alongcommunication links between the trading centers. Placement of serversfor controlling execution of a distributed trade in this manner mayreduce the latency of information propagation during the trade relativeto conventional techniques. This is illustrated using space-timediagrams shown in FIGS. 4 and 5.

FIG. 4 shows a space-time diagram 400 of a conventional implementationof a distributed transaction comprising buying a first financialinstrument at trading center 410 and selling a second financialinstrument at trading center 420. In this example, the trade iscontrolled at trading center 410. For the purposes of this illustrationit is assumed that the latency of information propagation between thetwo trading centers is τ.

In FIG. 4, trading center 410 sends information about a first financialinstrument (traded at trading center 410) to trading center 420 at timet=−τ. Similarly, trading center 420 sends information about a secondfinancial instrument (traded at trading center 420) to trading center410 at time t=−τ. The information may be any suitable information aboutthe financial instruments that may be used to determine what tradeshould be made. For instance, the information may comprise informationrelated to prices of the financial instruments (e.g., log-prices).

Trading center 420 may receive information sent from trading center 410at time t=0. Similarly, trading center 410 may receive information sentfrom trading center 420 at time t=0. Based upon the receivedinformation, trading center 410 may execute a trade (e.g., to buy anamount of the first financial instrument) and may send tradeinstructions to trading center 420 (e.g., for an order to sell an amountof the second financial instrument). Trading center 420 may receivetrade instructions from trading center 410 at time t=τ and may executethe trade specified by the instructions. Thus, the conventional approachrequires time of at least 2τ in order to execute the distributedtransaction.

FIG. 5 shows a space-time diagram 500 of distributed transactiondescribed with reference to FIG. 4, but executed on server 530 locatedat an intermediate location along the communication link between tradingcenters 510 and 520. For the purposes of this illustration, it isassumed that the latency of information propagation between the tradingcenters is τ (as before) and that the latency of information propagationbetween trading center 510 and server 530 is Δt. Accordingly, thelatency of information propagation between server 530 and trading center520 is τ−Δt.

In FIG. 5, trading center 510 may send information about a firstfinancial instrument at time t=−Δt to server 530, and trading center 520may send information about a second financial instrument at timet=−(τ−Δt) to server 530. The information may be any suitable informationabout the financial instruments that may be used by server 530 todetermine what trade should be made. For instance, the information maycomprise information related to prices of the financial instruments(e.g., log-prices).

Server 530 may receive both pieces of information at time t=0. Basedupon the received information, server 530 may send trade instructions totrading center 510 (e.g., instructions for an order to buy an amount ofthe first financial instrument) and may send trade instructions totrading center 520 (e.g., instructions for an order to sell an amount ofthe second financial instrument).

Trading center 510 may receive trade instructions from server 530 attime t=Δt and trading center 520 may receive trade instructions fromserver 530 at time t=(τ−Δt). Accordingly, in this case, the amount oftime required to execute the distributed transaction is either 2 Δt or2(τ−Δt), whichever is larger. Thus, the round trip delay may be as lowas τ in this case. This improvement may be a significant improvement inthe case of high-frequency trading.

FIG. 6 shows an illustrative process for controlling execution of adistributed trading strategy for trading financial instruments atmultiple trading centers. Process 600 may be executed by a serveroperatively coupled to one or more communication links among themultiple trading centers and may control execution of the tradingstrategy by sending trade instructions to one or more trading centers.For example, process 600 may be executed by server 106 in system 100and/or by server 306 in system 300.

Control over execution of a distributed trading strategy at multipletrading centers may comprise receiving information about one or morefinancial instruments traded at one of the multiple trading centersand/or sending trade instructions for trading these financialinstruments. Trade instructions may be sent in response to tradeconditions being met, which may be determined based on information aboutthe financial instruments received from one or more of the multipletrading centers. Trade instructions sent to one trading center may becryptographically signed and may include trade instructions sent toanother trading center.

Process 600 begins when information about a first financial instrumentis received in act 602 and information about a second financialinstrument is received in act 604. The first and second financialinstruments may be any suitable financial instruments that may be tradedat a trading center and may be any of the financial instrumentspreviously mentioned with reference to FIG. 1. The first and secondfinancial instruments may be traded at a first trading center and asecond trading center, respectively. Accordingly, information about thefirst financial instrument may be received from the first trading centerand information about the second financial instrument may be receivedfrom the second trading center. In some instances, information about afinancial instrument (e.g., first and/or second financial instrument)may be received from any trading center at which that financialinstrument is traded. Though, in other instances, information about afinancial instrument may be received from a trading center at which thefinancial instrument is not traded. Still, in other instances,information about a financial instrument may be obtained from anysuitable entity, not necessarily a trading center, that may haveinformation about the financial instrument.

Regardless of the source of information about the first financialinstrument and the second financial instrument, received in acts 602 and604, such information may comprise any information related to trading ofthe corresponding financial instrument. The information may compriseinformation related to past and current prices of the financialinstrument and, for example, may comprise values indicative ofhistorical prices and/or current prices of the financial instrument. Forexample, the information may comprise historical and/or current pricesof the financial instrument. Additionally or alternatively, theinformation may comprise historical and/or current log-prices of thefinancial instrument. The information about a financial instrument mayinclude any other function of the historical and/or current prices suchas averages of prices and/or log prices over a (predetermined orautomatically identified) time-interval.

In some embodiments, information about a financial instrument maycomprise any quantity derived from historical and/or current prices ofthe financial instrument. For instance, it may include rates of return,information about trends in prices, and parameters of any modelsestimated from one or more historical and/or current prices. Theinformation may also comprise transaction costs associated with tradingthe financial instrument, bid-ask spreads, and trading requirements(e.g., purchase minimums and/or margin requirements). Numerous otherexamples exist (e.g., analyst reports, econometric indicators, financialinformation about an entity related to a financial security such as thecompany issuing a stock/bond or country whose currency is being traded).Many other examples will be apparent to those skilled in the art.

After receiving information about the first and the second financialinstrument, in acts 602 and 604, process 600 proceeds to decision block606 at which it is determined whether trade conditions are met. Thedetermination may be made based at least in part on the first and secondinformation received in acts 602 and 604. If it is determined that tradeconditions are met, the process proceeds to act 608, whereas if it isdetermined that trade conditions are not met, the process loops back tothe beginning and acts 602, 604, and 606 may be repeated until it isdetermined that trade conditions are met.

Trade conditions may be any suitable conditions that indicate whether itis appropriate to execute a trade. The trade may be a trade that may bemade as part of a trading strategy and the trade conditions may dependon the trading strategy. The trade conditions may comprise checkingconditions for the first financial instrument, for the second financialinstrument, or for both the first and the second financial instruments.For instance, a trading strategy may comprise buying the first financialinstrument (e.g., stock “ABC”) only when the price of the firstfinancial instrument falls below a predetermined threshold. Thethreshold may depend on the historical prices and may be an averageprice of the financial security over a time period. In this case, thetrade conditions may reflect this strategy and checking whether tradeconditions are met may comprise checking for an indication that theprice (or any suitable function of the price such as the log price) ofthe first financial instrument is below the predetermined thresholdbased on information about the first financial instrument received inact 602.

In another example, a trading strategy may comprise buying and sellingfinancial instruments in accordance with a statistical arbitragestrategy. For instance, a trading strategy may be a pairs tradingstrategy and may comprise buying the first trade instrument and sellingthe second instrument (or vice versa). In this case, checking whethertrade conditions are met may comprise checking when the price (or anysuitable function of the price such as the log price) of the firstfinancial instrument is above a first threshold and the price (or anysuitable function of the price such as the log price) of the secondfinancial instrument is below a second threshold. It should beappreciated that checking whether trade conditions are met may comprisechecking conditions based on any suitable information received in acts602 and 604 and is not limited to conditions based on prices and/or afunction thereof. Additionally or alternatively, trade conditions may bebased on information received prior to the beginning of the process(i.e., not just in acts 602 and 604).

Trade conditions may be specified by a user or may be automaticallydetermined by a computer. For instance, trade conditions may bespecified by user 112 described with respect to system 100 and server106, which may be executing process 600, may be configured to checkwhether these conditions are met based on information received fromtrading center 102 and trading center 110.

If it is determined, in decision block 606, that trade conditions aremet, trade instructions may be specified in act 608 of process 600.Trade instructions may comprise instructions for making trades atmultiple trading centers. For example, trade instructions may comprisefirst trade instructions for executing a trade (e.g., involving thefirst financial instrument) at the first trading center and may alsocomprise second trade instructions for executing a trade (e.g.,involving the second financial instrument) at the second trading center.For instance, in a pairs trading strategy, trade instructions maycomprise instructions for buying an amount of the first financialinstrument and instructions for selling an amount of the secondfinancial instrument. Further, the amount of each financial instrumentto buy/sell may depend on information about the first and/or secondfinancial instruments received in acts 602 and 604 of process 600.Though, trade instructions are not limited to specifying pairs and/orstatistical arbitrage trades and may be used to specify any distributedtrading strategy comprising trading at multiple trading centers. Assuch, trade instructions may be in any suitable format and may compriseany information required to instruct each trading center to make anytrades.

Once trade instructions are specified in act 608, trade instructions maybe sent to multiple trading centers. For instance, if trade instructionscomprise first trade instructions for trading a first financialinstrument at the first trading center, first trade instructions may besent to first trading center in act 610 of process 600. Similarly, iftrade instructions comprise second trade instructions for trading asecond financial instrument at the second instrument, second tradeinstructions may be sent to second trading center in act 612 of process600.

In acts 610 and 612, trade instructions may be sent using acommunication link between the first trading center and the secondtrading center. For example, if process 600 is executing on server 106of system 100, first trade instructions may be sent along communicationlink 104 to trading center 102 and second trade instructions may be sentalong communication link 104 to trading center 110. As another example,if process 600 is executing on server 306 of system 300, and server 306selects trading centers 302 and 310, then first trade instructions maybe sent along communication link 312 to trading center 302 and secondtrade instructions may be sent along communication link 312 to tradingcenter 310. Though, if server 306 selects trading centers 304 and 308,then first trade instructions may be sent along communication link 314to trading center 304 and second trading instructions may be sent alongcommunication link 314 to trading center 308.

In conventional trading, positions that at least partially offset oneother may incur reduced margin requirements (i.e., how much collateralneeds to be deposited in order to make a trade). For instance, marginrequirements may be reduced for trades that comprise taking both a longand a short position; mechanisms for taking long and short positions areknown in the art. The inventors have recognized that when such tradesoccur at a single trading center, it may be easy to verify that a tradecomprises taking both a long position and a short position, but this maynot be easy to verify when such a trade occurs at multiplegeographically-separated trading centers. The inventors have appreciatedthat in a distributing trading scenario, a dishonest trader may falselyclaim to implement a strategy for which margin requirements may bereduced. For example, a trader using server 106 of system 100 may sendfirst trade instructions to trading center 102 to take a long positionand falsely claim that he also sent trade instructions to the secondtrading center to take a short position, in order to get the benefit ofreduced margin requirements.

The inventors have recognized and appreciated that this problem may beaverted if audit information for the first trade could be provided.Audit information may comprise a guarantee of the second trade. Forinstance, in the context of process 600, audit information comprising aguarantee of the second trade may be provided to the first tradingcenter.

Accordingly, after first and second trade instructions are sent to thefirst and second trading centers in acts 610 and 612, process 600proceeds to decision block 614 during which it is determined whetheraudit information should be provided to the first trading center, thesecond trading center or both the first and second trading centers.

The determination whether to provide audit information to the firstand/or second trading center may be made based on any suitable criteria.For example, if first trade instructions sent to the first tradingcenter rely on reduced margin requirements, it may be determined thataudit information should be provided to the first trading center.Though, this determination may be made in any suitable way as the way inwhich this determination is made is not a limitation of the presentinvention.

If it is determined, in act 614, that audit information for the firstand/or second trading center should not be provided, process 600completes.

On the other hand, if it is determined, in act 614, that auditinformation for the first and/or second trading center should beprovided, such audit information may be created and cryptographicallysigned in act 616. Audit information for the first trading center maycomprise a guarantee that second trade instructions specify a trade, atthe second trading center, that creates an offset position to theposition created by the trade at the first trading center specified bythe first trade instructions. For instance, audit information for thefirst trading center may comprise second trade instructions. Similarly,audit information for the second trading center may comprise a guaranteethat first trade instructions specify a trade, at the first tradingcenter, that may create an offset position to the position created bythe trade at the second trading center specified by the second tradeinstructions. For instance, audit information for the second tradingcenter may comprise first trade instructions.

Audit information may be cryptographically signed using any suitabletechnique as known in the art. For instance, audit information may besigned using any asymmetric cryptographic technique.

After audit information is created in act 616, it may be transmitted tothe first and/or the second trading center in act 618 of the process600. Audit information may be transmitted to the trading center(s) inthe same way that trade instructions are transmitted to the tradingcenter (e.g., using a communication link between the first and secondtrading centers). After audit instructions are sent to the first and/orsecond trading center, process 600 completes.

It should be recognized that process 600 is an illustrative process andthat various modifications of process 600 are possible. For example,though process 600 was described with respect to a distributed tradingstrategy in which two financial instruments are traded, process 600 isnot limited in this respect and may be applied to trading more than twofinancial instruments. Moreover, though process 600 was described withrespect to a distributed trade using two trading centers (first andsecond trading center), the process may be adapted to control executionof a trade distributed across more than two trading centers. As anotherexample, audit information may be sent concurrently with the first tradeinstructions and/or the second trade instructions instead of being sentafter the first and the second trade instructions.

Process 600 may be executed at a server located at an intermediatelocation between the first and second trading center. For instance, asdescribed with reference to FIG. 1 and FIG. 3, the server may be locatedat a predetermined location along a communication link between a pair oftrading centers. Thus, the server at the predetermined location maycontrol execution of a trading strategy and may send instructions to thefirst trading center and the second trading center to trade the firstand the second financial instrument. The location of the server may bedetermined prior to execution of process 600 and may be determined basedon a number of factors including properties of the communication linkbetween the first trading center and the second trading center,characteristics of the first financial instrument and the secondfinancial instrument, and the trading strategy.

FIG. 7 is a flowchart of an illustrative process 700 for calculating alocation to place the server. Process 700 may be executed using aprocessor and may be performed by or on behalf of any entity that maywish to install and/or configure a server to control execution of adistributed trade at some location along a communication link betweentrading centers. The entity may be an infrastructure provider such asnetwork provider, a trading platform provider, a financial institution,operator of a trading center. Though any entity may perform process 700,as the invention is not limited in this respect.

Process 700 begins when one or more characteristics of a first financialinstrument traded at a first trading center, and one or morecharacteristics of a second financial instrument, traded at a secondtrading center, are obtained in acts 702 and 704, respectively.

Characteristics of the first and second financial instruments may beobtained from any suitable source. In some instances, they may beobtained from any trading center at which these instruments are traded(e.g., the first and second trading center). In other instances, theymay be derived from any historical data (e.g., historical prices) of thefinancial instrument using any suitable technique or from any otherinformation related to the financial instrument.

In some embodiments, characteristics of the first financial instrument,obtained in act 702, may be the same as the characteristics of thesecond financial instrument, obtained in act 704. Though, in otherembodiments, characteristics of the first financial instrument, obtainedin act 702, may be different from the characteristics of the secondfinancial instrument, obtained in act 704, as the invention is notlimited in this respect.

Regardless of how the characteristics of the first and second financialinstrument are obtained, each obtained characteristic may be anycharacteristic indicative of the behavior of the financial instrument.The characteristic may be any characteristic indicative of the behaviorof the prices of the financial instrument and may be any function of thehistorical, current, and future predicted prices of the financialinstrument. For instance, a characteristic may be a reversion rate ofthe financial instrument or the volatility of the financial instrument.

A reversion rate of a financial instrument may be indicative of the rateat which the prices of a financial instrument (or a function thereof)revert to exhibiting a trend from which they may have deviated. Thetrend may be any of numerous trends as known in the art—the trend may bea constant such as an average of the instrument's prices (or a functionthereof) calculated over a period of time. In this case, the reversionrate is referred to as the mean reversion rate, which is the rate atwhich the prices of the instrument (or a function thereof) revert to theaverage price (or a corresponding function thereof). The trend may beany polynomial trend such as a linear trend or a quadratic trend. Insome instances, the trend may not be a deterministic trend and may be astochastic trend such as a random walk or a stationary stochasticprocess obeying certain characteristics.

It should be recognized that reversion rate and volatility are onlyexamples of characteristics that may be used and that many othercharacteristics of financial instruments may be employed. An examplecharacteristic of a financial instrument may be a statistic of theinstrument's prices over a time period and may be the average of theprices, standard deviation of the prices, and kurtosis of the prices.Another example of a characteristic of a financial instrument may be astatistic of the instrument's returns (e.g., any moment of the returns).Another example may be a trend in the instrument's prices (or a functionof the prices). Another example of a characteristic of one financialinstrument (e.g., derivative) may be a characteristic of anotherinstrument related to the instrument (e.g., the financial instrument onwhich the derivative is based).

Yet another example of a characteristic may be a characteristic that isa function of both the first and the second financial instruments. Inthis case, the characteristic may be indicative of the relationshipbetween the first and second financial instruments. For instance, if thefirst and second financial instruments are cointegrated, thecharacteristic may be the cointegrating vector. If, the first and secondfinancial instruments are correlated, then the characteristic may beindicative of a degree of correlation (e.g., a cross-correlationcoefficient) between the two instruments.

Process 700 next continues in act 706, when a property of thecommunication link between the first trading center and the secondtrading center is obtained. The property may be any property indicativeof the latency of propagation of information along the communicationlink. For instance, the property may be the latency of propagation of anelectromagnetic signal through the communication link. In the case thatthe communication link comprises fiber optic cable, the property of thecommunication link may be the latency of propagation of light throughthe fiber-optic cable or may be the index of refraction of thefiber-optic cable. In the case that the communication link comprises anyphysical link (e.g., another type of cable) or any equipment (e.g.,repeaters, amplifiers, relays, satellites, radios, etc.), the propertymay be any property related to the link or the equipment. The propertymay also be any property indicative of the usage of a communicationlink. For instance, the property may be related to the level of networkcongestion.

The property may be obtained in any suitable manner. In some cases theproperty may be known in advance (e.g., index of refraction of afiber-optic cable), while in other cases the property may be measured.The property may be measured and may be obtained either passively oractively. For instance, passive measurements of communications along thecommunication link may be used to determine the property. Additionallyor alternatively, the communication link may be actively probed (e.g.,by sending out test messages/packets from a computer connected to thecommunication link and calculating the time required for a response tocome back to the computer).

After one or more characteristics of each of the first and secondfinancial instruments and at least one property of the communicationlink are obtained, the location to place the server for controlling adistributed trading strategy may be determined in act 708 of process700. The location may be determined by using a criterion that depends onat least a portion of this information. In some instances, the criterionmay depend both on a property of the communication link and/or acharacteristic of one or both of the first and second financialinstruments. The criterion may be any function of the values of thecharacteristics and/or property of the communication link and mayassociate a score with each potential location of the server along thecommunication link.

The location may be computed as the location along the communicationlink associated with the highest score computed by using theabove-mentioned criterion. Though, in some embodiments, the location maynot be the location associated with the highest score. For instance, insome cases it may be possible to place a server only at one of a set ofpredetermined locations along the communication link between the firstand the second trading center. In this case, the location may beselected from the set of location based on the scores associated withthese locations, and may be selected as the location with the highestscore.

For example, the characteristics of the first and second financialinstruments may be reversion rates (e.g., mean-reversion rates)associated to each of the instruments, the property may be the latencyof propagation of information from the first trading center to thesecond trading center, and the trading strategy may be a pairs tradingstrategy (e.g., buy an amount of the first financial instrument at thefirst trading center and sell an amount of the second financialinstrument at the second trading center). The criterion may be afunction of the reversion rates and the latency of propagation and mayindicate a time to execute a trade according to the pairs tradingstrategy.

In this example, the criterion may be used to compute a score for eachtime to enter the pairs trading strategy (e.g., when a ratio of prices(or a ratio of some function of the prices) of the financial instrumentsdeviates from a historical value). The time associated with the highestscore may be the time to enter into the pairs trade. In turn, this timemay be used together with the latency of information propagation todetermine the location for the server. Though it should be recognized,that this example is merely illustrative and that any or all elements ofthis example, including the characteristics of the financialinstruments, the property of the communication link, the criterion, andthe trading strategy, may be varied. Any suitable approach todetermining the location of a server based on characteristics of thefirst and second financial instruments and property of the communicationlink may be used.

In one illustrative example, the location of the server may be computedas described below. Consider the situation in which the log-prices of afirst financial instrument traded at a first trading center and a secondfinancial instrument traded at a second trading center are modeled bydecoupled Vasicek processes according to:dx(t)=−a _(x) x(t)dt+σ _(x) dV(t),dy(t)=a _(y) y(t)dt+σ _(y) dW(t),In the above expression, a_(x) and a_(y) may be values indicative of aspeed of reversion of the first and second financial instruments,respectively. Variables σ_(x) and σ_(y) may be values indicative of theinstantaneous volatilities of the first and second financialinstruments, respectively. Though, it should be appreciated, that theabove decoupled Vasicek process model may be used to model the temporalevolution of any trading signal associated with the first and secondfinancial instruments and is not limited to modeling the temporalevolution of log-prices as in this illustrative example. For instance,prices or any suitable function of the prices may be modeled using thismodel.

Now suppose that the latency of propagation of information between thefirst trading center and the second trading center is given by cτ, wherec is the speed of propagation through the communication link between thefirst and second trading centers. We wish to determine a location for aserver to be placed along the communication link between the firsttrading center and the second trading center. As previously discussed,this location may be determined based on characteristics of the firstand second financial instrument (e.g., the reversion rates a_(x) anda_(y)), the latency of propagation between the first trading center andthe second trading center (which depends on τ), and the trading strategy(e.g., statistical arbitrage trade, pairs trade, etc.)

In the case of a pairs trade using the first financial instrument andthe second financial instrument, it is known in the art that a pairstrade may be triggered when the ratio between the log-prices (or othertrading signal) of the financial instruments is large. Accordingly, alocation may be chosen in order to maximize this ratio. Though, manyother criteria for selecting a location may be possible and may be basedon a strategy that would maximize profit for that strategy.

Assume, without loss of generality, that x(−Δt)>y(−(τ−Δt)), such thatthe objective is to find a value of Δt to maximize the quantity:e ^(R(Δt)) ≡e ^(x(Δt)) /e ^(y(τ−Δt))

Then the server will be located along the communication link at alocation represented by c^(Δt), which indicates the latency ofpropagation of information from the first trading center to the server.The solution may be obtained as follows. From the perspective of theserver at t=0, the Vasicek expectation values of x(t) and y(t) willdecay exponentially back to the mean from instantaneously known valuesx(−Δt), y(−(τ−Δt)):

R(Δt)

=x(−Δt)e ^(−2a) ^(x) ^(Δt) −y|(−(τ−Δt))e ^(−2a) ^(y) ^((τ−Δt))

The above expected security ratio will reach an extremum when Δtsatisfies:

$0 = {\frac{\mathbb{d}\left\langle {R\left( {\Delta\; t} \right)} \right\rangle}{{\mathbb{d}\Delta}\; t} = {{- {{\mathbb{e}}^{{- 2}\; a_{x}\Delta\; t}\left( {\overset{.}{X} + {2\; a_{x}X}} \right)}}❘{- {{\mathbb{e}}^{{- 2}\;{a_{y}{({\tau - {\Delta\; t}})}}}\left( {\overset{.}{Y} + {2\; a_{y}Y}} \right)}}}}$where${X \equiv {x\left( {{- \Delta}\; t} \right)}},{\overset{.}{X} \equiv {\overset{.}{x}\left( {{- \Delta}\; t} \right)}},{Y \equiv {{y\left( {- \left( {\tau - {\Delta\; t}} \right)} \right)}\mspace{14mu}{and}\mspace{11mu}\overset{.}{\; Y}} \equiv {{\overset{.}{v}\left( {- \left( {\tau - {\Delta\; t}} \right)} \right)}.}}$

Solving for the intermediate position, two solution cases depending onthe instantaneous behavior of the first and second financial instrumentsresults. The special case is given by:{dot over (X)}+2a _(x) X=0={dot over (Y)}+2a _(y) Yand the general case is given by:

$\frac{\Delta\; t}{\tau} = {\frac{a_{y}}{a_{x} + a_{y}} + {\frac{1}{2\left( {a_{x} + a_{y}} \right)\tau}{\ln\left\lbrack {- \frac{\overset{.}{X} + {2\; a_{x}X}}{{\overset{.}{Y} + {2\; a_{y}Y}}\;}} \right\rbrack}}}$

To test for concavity in the general case, calculate:

${{0 > \frac{\mathbb{d}^{2}\left\langle {R\left( {\Delta\; t} \right)} \right\rangle}{{\mathbb{d}\Delta}\; t^{2}}} = {{{\mathbb{e}}^{{- 2}\; a_{x}\Delta\; t}\left\lbrack {{2\;{a_{x}\left( {\overset{.}{X} + {2\; a_{x}X}} \right)}} + \overset{¨}{X} + {2\; a_{x}\overset{.}{X}}} \right\rbrack} - {{\mathbb{e}}^{{- 2}\;{a_{y}{({\tau - {\Delta\; t}})}}}\left\lbrack {{2\;{a_{y}\left( {\overset{.}{Y} + {2\; a_{y}Y}} \right)}} + \overset{¨}{Y} + {2\; a_{y}\overset{.}{Y}}} \right\rbrack}}},$where: {umlaut over (X)}≡{umlaut over (x)}(−Δt) and Ÿ≡ÿ(−(τ−Δt)).Accordingly, it follows that there will be a local maximum at Δt whenthe following inequality is satisfied:4a _(x) ² X+4a _(x) {dot over (X)}+{umlaut over (X)}<0<4a _(y) ² Y+4a_(y) {dot over (Y)}+Ÿ.

These conditions may be satisfied when fluctuations in the log prices ofthe first and second financial instrument are sufficiently sharp. Forinstance, fluctuations whose characteristic frequency f lies in therange:

$\frac{\max\left( {a_{x},a_{y}} \right)}{\pi} < f < {\frac{\tau^{- 1}}{\pi\sqrt{2}}.}$

Such fluctuations may be common in conventional high-frequency trading.For instance, for maximally distant points on Earth τ≈67 ms, and fortrading centers τ may be even smaller (e.g., τ≈1.1 ms for tradingcenters located in London and Paris). In this illustrative example,these latencies imply lower bounds on the characteristic time between“exploitable” fluctuations f⁻¹, of approximately 300 ms for maximallydistant trading centers, approximately 5 ms for trading centers locatedin London and Paris, and lower for multiple markets within one city. Incontrast, reversion times (which determine approximate values of a_(x)⁻¹ and a_(y) ⁻¹) are typically longer. Consequently, the range given bythe above equation is a wide range and may include the typical timescales exploited in high-frequency trading (e.g., 10 ms-10 s range).

It should be noted that under the simplifying assumption that thefluctuations

$\left. {\left( {{\frac{\overset{.}{X}}{X}} \sim {2\;\pi\; f} \gg {2\;{\max\left( {a_{x},a_{y}} \right)}}} \right\rbrack:} \right),$are high-frequency fluctuations the solution for the general casereduces to:Δt=τa _(y)/(a _(x) +a _(y)).In this case, the location of the server may be determined by weightingthe latency of information propagation through the communication link bya value derived from the characteristic of the first financialinstrument and the characteristic of the second financial instrument. Inthis illustrative example, the value may be given by the ratio of thereversion speed of the second financial instrument and the sum of thereversion rates of the first financial instrument and the secondfinancial instrument.

It should be recognized that the above-illustrated calculations for thecase of log-prices of two financial instruments were merely illustrativeand that analogous calculations may be made in any of numerous othercases. For instance, similar calculations may be made for any functionof the prices of the two financial instruments and by using models otherthan the Vasicek model to model the temporal behavior of each financialinstrument. In a case, when a trading strategy is based on volatility ofthe financial instruments, Ornstein-Uhlenbeck processes and theirrefinements may be used to model stochastic volatility.

After the location for the server is calculated in at 708 of process700, the process proceeds to decision block 710 in which it may bedetermined that at least a portion of the information about thefinancial instruments and/or the communication link may be updated. Forinstance, the characteristics of the financial instruments may beupdated and/or the property of the communication link may be updated.This determination may be made in any suitable way. For instance, it maybe determined that information should be updated if it is detected thatutilization of the communication link has changed. Though the manner inwhich this determination is made is not a limiting aspect of the presentinvention.

If it is determined in decision block 710 that at least a portion of theinformation should be updated, process 700 loops back to act 702 andacts 702-708 are repeated. Thus, in acts 702-706 updated informationrelated to the first and second financial instruments and thecommunication link may be obtained and the location of the server may berecalculated based on the updated information in act 708.

If it is determined that the information need not be updated, process700 proceeds to act 712 in which the server is configured to communicatewith the first trading center and the second trading center. The servermay be installed and operatively coupled to the communication link atthe calculated location. The server may be installed at or near thecalculated location such that the latency of information propagationbetween the server and the first trading center is substantially thelatency of information propagation between the calculated location andthe first trading center.

In some embodiments, the server may already be physically installed atthe location calculated in act 708. This may be the case, for example,when one of a predetermined set of locations is selected and eachlocation in the set corresponds to a location which has a server alreadyinstalled). Alternatively, the server may need to be physicallyinstalled at the calculated location. In either case, the server may beconfigured to communicate with the first and second trading center byusing the communication link. The server may be configured manually(e.g., by a network technician) or may be configured automatically by acomputer. After the server is configured for communication with thefirst and second trading center, process 700 completes. The configuredserver may now be used to control execution of distributed trades. Forinstance, the configured server may be used to execute process 600.

It should be recognized that process 700 is an illustrative process andthat many modifications of process 700 are possible. For example, thoughonly one property of the communication link was obtained in act 706,process 700 is not so limited and any number of properties of thecommunication link may be obtained and used to calculate the location ofthe server. Moreover, though process 700 was described with respect to atwo trading centers (first and second trading center) and two financialinstruments, the process may be easily adapted calculate the location ofthe server based on properties of communication links among more thantwo trading centers and based on characteristics of more than twofinancial instruments.

When a location of a server to control the execution of a distributedtrade is fixed, the above-described techniques may be used to selecttrading centers on which to execute the distributed trade. In someembodiments, the server may be configured to select a pair of tradingcenters among a set of trading centers and, subsequently, may controlthe execution of a distributed trade on the selected trading centers.

FIG. 8 is a flowchart of an illustrative process 800 for calculating apair of trading centers for trading a first and a second financialinstrument. Process 800 may be executed using a processor and may beexecuted at a server located at an intermediate location along acommunication link between one trading center and another tradingcenter. Additionally, the server may also be located at an intermediatelocation along another communication link between a pair of tradingcenters. For instance, illustrative process 800 may execute on server306 of system 300.

Process 800 begins when one or more characteristics of a first financialinstrument traded at a first trading center, and one or morecharacteristics of a second financial instrument, traded at a secondtrading center, are obtained in acts 802 and 804, respectively.Characteristics of the first and second financial instruments may beobtained from any suitable source and may be any suitablecharacteristics. For example, characteristics of the first and secondfinancial instruments may be obtained from any trading center at whichthese instruments are traded, derived from historical data and/orobtained from a third party. For example, the obtained characteristicsmay be any of the characteristics described with reference to FIG. 7,and each obtained characteristic may be any characteristic indicative ofthe behavior of the financial instrument.

Process 800 next continues in act 806, when one or more properties ofone or more communication links may be obtained. Each communication linkmay be a communication link between a pair of trading centers. Eachcommunication link may be a link to which a server to control executionof a distributed trading strategy is coupled. The server may beoperatively coupled to the link at an intermediate location between thetrading centers connected by the link. For example, properties ofcommunication links 312 and 314 illustrated in FIG. 3 may be obtained,in act 806. It should be recognized that properties need not be obtainedfor every communication link to which a server may be coupled and may beobtained only for some of the communication links. For example, one ormore properties associated with communication link 314 may be obtained,but no properties associated with communication link 312 may beobtained.

The one or more properties obtained in act 806 may be any suitableproperties. For instance, a property indicative of the latency ofpropagation of information along the communication link may be obtained.Each obtained property may also be any property described with referenceto FIG. 7 and may be obtained from any suitable source such as any ofthe sources described with reference to FIG. 7.

After one or more characteristics of each of the first and secondfinancial instruments and one or more properties of one or morecommunication links are obtained, a pair of trading centers for tradingthe first and second financial instrument may be selected. The pair oftrading centers may comprise a trading center at which the firstfinancial instrument is traded and a trading center at which the secondfinancial instrument is traded. Though, in some instances, the first andsecond financial instruments may be traded together on one or both ofthe trading centers.

The selection may be made by using a criterion that depends on theobtained characteristics of the financial instruments, obtained propertyor properties of the one or more communication links. The criterion mayalso depend on the location of the server used to control the executionof a distributed trade involving the first and second financialinstruments. For instance, the criterion may depend on the location ofserver 306 described with reference to FIG. 3. In particular, sinceserver 306 is operatively coupled to communication links 312 and 314 at(or near) locations 316 and 318, respectively, the criterion may dependon locations 316 and 318.

In some embodiments, the trading centers may be selected by evaluating acriterion for every pair of considered trading centers. The value of thecriterion may be used to select one of the pairs of considered tradingcenters. For instance, the criterion may be used to evaluate tradingcenters 302 and 310, and trading centers 304 and 308. The valuescomputed for each of these two pairs may be used to select one of thesetwo pairs of trading centers.

In some embodiments, a server location may be computed for eachconsidered pair of trading centers, and the pair associated with thelocation closest to the location of the server (e.g., server 306) may beselected. The location for a server may be computed using theinformation obtained in acts 802-806 of process 800 and may be done inaccordance with process 700 described with reference to FIG. 7.

Process 700 may be used to compute a location of a first server along afirst communication link between a first pair of trading centers and alocation of a second server along a second communication link between asecond pair of trading centers. The computed locations may be used todetermine whether the first or the second pair of trading centers shouldbe selected. For instance, the first pair of trading centers may beselected if is determined that the distance between the first serverlocation and the location of the server controlling the execution of adistributed trade (e.g., server 306) is small than the distance betweenthe second server location and the location of the server. Any suitabledistance measure may be used.

For instance, process 700 may be used to compute a location for a firstserver along communication link 312 and a location for a second serveralong communication 314. These locations may be computed based oncharacteristics of the first and second financial instruments (e.g.,mean-reversion rates) and based on properties of communication links 312and 314 (e.g., latency of propagation of information along the link).Then, trading centers 302 and 310 may be selected, in act 808, if it isdetermined that the distance between computed location of the firstserver and location 316 is smaller than the distance between thecomputed location of the second server and location 318.

After a pair of trading centers is selected in act 808 of process 800,the process proceeds to decision block 810 in which it may be determinedthat at least a portion of the information about the financialinstruments and/or the communication link(s) may be updated. Aspreviously mentioned, characteristics of the financial instruments maybe updated and/or the properties of the communication link(s) may beupdated. The manner in which this determination is made is not alimiting aspect of the present invention.

If it is determined in decision block 810 that at least a portion of theinformation should be updated, process 800 loops back to act 802 andacts 802-808 are repeated. Thus, in acts 802-806 updated informationrelated to the first and second financial instruments and thecommunication link may be obtained and a different pair of tradingcenters may be selected based on the updated information in act 808.

If it is determined that the information need not be updated, process800 proceeds to act 812, in which the server (e.g., server 306) isconfigured to communicate with the trading centers in the selected pair.At this point, the configured server may be used to control theexecution of a distributed trading strategy using trading centers in theselected pair of trading centers. For example, the configured server maybe used to execute process 600.

It should be recognized that process 800 is an illustrative process andthat many modifications of process 800 are possible. Though process 800was described with respect to selecting a pair of trading centers andtwo financial instruments, the process may be adapted to select anynumber of trading centers from a set of trading centers and may selecttrading centers based on characteristics any suitable number offinancial instruments.

Though we described with respect to financial applications, embodimentsof the present disclosure may be applied to a wide variety of problemsin other domains. Techniques disclosed herein may be applied to anysetting which comprises time-sensitive calculations performed atgeographically distributed locations. For instance, techniques describedherein may be adapted for video-teleconferencing, virtual reality, andnetworking applications, to name only a few.

The above-described embodiments of the present invention can beimplemented in any of numerous ways. For example, the embodiments may beimplemented using hardware, software or a combination thereof. Whenimplemented in software, the software code may be executed on anysuitable processor or collection of processors, whether provided in asingle computer or distributed among multiple computers.

It should be appreciated that a computer may be embodied in any ofnumerous forms, such as a rack-mounted computer, a desktop computer, alaptop computer, or a tablet computer. Additionally, a computer may beembodied in a device not generally regarded as a computer, but withsuitable processing capabilities, including a Personal Digital Assistant(PDA), a smart phone or any other suitable portable or fixed electronicdevice.

Also, a computer may have one or more input and output devices. Thesedevices may be used, among other things, to present a user interface.Examples of output devices that may be used to provide a user interfaceinclude printers or display screens for visual presentation of output,and speakers or other sound generating devices for audible presentationof output. Examples of input devices that may be used for a userinterface include keyboards, microphones, and pointing devices, such asmice, touch pads, and digitizing tablets.

Such computers may be interconnected by one or more networks in anysuitable form, including a local area network (LAN) or a wide areanetwork (WAN), such as an enterprise network, an intelligent network(IN) or the Internet. Such networks may be based on any suitabletechnology and may operate according to any suitable protocol and mayinclude wireless networks, wired networks, and/or fiber optic networks.

An illustrative implementation of a computer system 900 that may be usedin connection with any of the embodiments of the invention describedherein is shown in FIG. 9. The computer system 900 may include one ormore processors 910 and one or more non-transitory computer-readablestorage media (e.g., memory 1120 and one or more non-volatile storagemedia 930). The processor 910 may control writing data to and readingdata from the memory 920 and the non-volatile storage device 930 in anysuitable manner, as the aspects of the invention described herein arenot limited in this respect. To perform any of the functionalitydescribed herein, the processor 910 may execute one or more instructionsstored in one or more computer-readable storage media (e.g., the memory920), which may serve as non-transitory computer-readable storage mediastoring instructions for execution by the processor 910.

The various methods or processes outlined herein may be coded assoftware that is executable on one or more processors that employ anyone of a variety of operating systems or platforms. Additionally, suchsoftware may be written using any of numerous suitable programminglanguages and/or programming or scripting tools, and also may becompiled as executable machine language code or intermediate code thatis executed on a virtual machine or a suitable framework.

In this respect, various inventive concepts may be embodied as at leastone non-transitory computer readable storage medium (e.g., a computermemory, one or more floppy discs, compact discs, optical discs, magnetictapes, flash memories, circuit configurations in Field Programmable GateArrays or other semiconductor devices, etc.) encoded with one or moreprograms that, when executed on one or more computers or otherprocessors, implement the various embodiments of the present invention.The non-transitory computer-readable medium or media may betransportable, such that the program or programs stored thereon may beloaded onto any computer resource to implement various aspects of thepresent invention as discussed above.

The terms “program” or “software” are used herein in a generic sense torefer to any type of computer code or set of computer-executableinstructions that can be employed to program a computer or otherprocessor to implement various aspects of embodiments as discussedabove. Additionally, it should be appreciated that according to oneaspect, one or more computer programs that when executed perform methodsof the present invention need not reside on a single computer orprocessor, but may be distributed in a modular fashion among differentcomputers or processors to implement various aspects of the presentinvention.

Computer-executable instructions may be in many forms, such as programmodules, executed by one or more computers or other devices. Generally,program modules include routines, programs, objects, components, datastructures, etc. that perform particular tasks or implement particularabstract data types. Typically the functionality of the program modulesmay be combined or distributed as desired in various embodiments.

Also, data structures may be stored in non-transitory computer-readablestorage media in any suitable form. For simplicity of illustration, datastructures may be shown to have fields that are related through locationin the data structure. Such relationships may likewise be achieved byassigning storage for the fields with locations in a non-transitorycomputer-readable medium that convey relationship between the fields.However, any suitable mechanism may be used to establish relationshipsamong information in fields of a data structure, including through theuse of pointers, tags or other mechanisms that establish relationshipsamong data elements.

Also, various inventive concepts may be embodied as one or more methods,of which an example has been provided. The acts performed as part of themethod may be ordered in any suitable way. Accordingly, embodiments maybe constructed in which acts are performed in an order different thanillustrated, which may include performing some acts simultaneously, eventhough shown as sequential acts in illustrative embodiments.

All definitions, as defined and used herein, should be understood tocontrol over dictionary definitions, definitions in documentsincorporated by reference, and/or ordinary meanings of the definedterms.

The indefinite articles “a” and “an,” as used herein in thespecification and in the claims, unless clearly indicated to thecontrary, should be understood to mean “at least one.”

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified. Thus, as anon-limiting example, “at least one of A and B” (or, equivalently, “atleast one of A or B,” or, equivalently “at least one of A and/or B”) canrefer, in one embodiment, to at least one, optionally including morethan one, A, with no B present (and optionally including elements otherthan B); in another embodiment, to at least one, optionally includingmore than one, B, with no A present (and optionally including elementsother than A); in yet another embodiment, to at least one, optionallyincluding more than one, A, and at least one, optionally including morethan one, B (and optionally including other elements); etc.

The phrase “and/or,” as used herein in the specification and in theclaims, should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases. Multiple elements listed with“and/or” should be construed in the same fashion, i.e., “one or more” ofthe elements so conjoined. Other elements may optionally be presentother than the elements specifically identified by the “and/or” clause,whether related or unrelated to those elements specifically identified.Thus, as a non-limiting example, a reference to “A and/or B”, when usedin conjunction with open-ended language such as “comprising” can refer,in one embodiment, to A only (optionally including elements other thanB); in another embodiment, to B only (optionally including elementsother than A); in yet another embodiment, to both A and B (optionallyincluding other elements); etc.

As used herein in the specification and in the claims, “or” should beunderstood to have the same meaning as “and/or” as defined above. Forexample, when separating items in a list, “or” or “and/or” shall beinterpreted as being inclusive, i.e., the inclusion of at least one, butalso including more than one, of a number or list of elements, and,optionally, additional unlisted items. Only terms clearly indicated tothe contrary, such as “only one of” or “exactly one of,” or, when usedin the claims, “consisting of,” will refer to the inclusion of exactlyone element of a number or list of elements. In general, the term “or”as used herein shall only be interpreted as indicating exclusivealternatives (i.e. “one or the other but not both”) when preceded byterms of exclusivity, such as “either,” “one of,” “only one of,” or“exactly one of.” “Consisting essentially of,” when used in the claims,shall have its ordinary meaning as used in the field of patent law.

Use of ordinal terms such as “first,” “second,” “third,” etc., in theclaims to modify a claim element does not by itself connote anypriority, precedence, or order of one claim element over another or thetemporal order in which acts of a method are performed. Such terms areused merely as labels to distinguish one claim element having a certainname from another element having a same name (but for use of the ordinalterm).

The phraseology and terminology used herein is for the purpose ofdescription and should not be regarded as limiting. The use of“including,” “comprising,” “having,” “containing”, “involving”, andvariations thereof, is meant to encompass the items listed thereafterand additional items.

Having described several embodiments of the invention in detail, variousmodifications and improvements will readily occur to those skilled inthe art. Such modifications and improvements are intended to be withinthe spirit and scope of the invention. Accordingly, the foregoingdescription is by way of example only, and is not intended as limiting.The invention is limited only as defined by the following claims and theequivalents thereto.

What is claimed is:
 1. A system for identifying a physical locationalong a communication link between a first trading center and a secondtrading center at which to couple to the communication link a server forsending trading instructions to the first trading center and/or thesecond trading center, the system comprising: at least one processorconfigured to: obtain a property of the communication link; and identifythe physical location at which to physically couple the server to thecommunication link at least in part by calculating a location based atleast in part on the obtained property of the communication link and atleast one characteristic of a first financial instrument traded at thefirst trading center, wherein the at least one characteristic of thefirst financial instrument includes a rate at which a value depending ona price of the first financial instrument moves to its long term trendover a predetermined period of time.
 2. The system of claim 1, whereinthe at least one processor is configured to calculate the location basedat least in part on the at least one of characteristic of the firstfinancial instrument traded at the first trading center and at least onecharacteristic of a second financial instrument traded at the secondtrading center.
 3. The system of claim 1, wherein the first financialinstrument is a financial instrument selected from the group consistingof an equity, a derivative, a fixed-income product, and a currency. 4.The system of claim 1, wherein the at least one characteristic of thefirst financial instrument depends on historical prices of the firstfinancial instrument.
 5. The system of claim 1, wherein the property ofthe communication link is a latency of electromagnetic signalpropagation through the communication link.
 6. The system of claim 1,wherein the server coupled to the communication link at the identifiedphysical location is configured to: send first trade instructions fortrading the first financial instrument to the first trading center; andsend second trade instructions for trading a second financial instrumentto the second trading center.
 7. The system of claim 6, wherein theserver coupled to the communication link at the identified physicallocation is further configured to: determine whether trade conditionsare met based at least in part on information associated with the firstfinancial instrument, and send the first trade instructions to the firsttrading center and the second trade instructions to the second tradingcenter, if it is determined that the trade conditions are met.
 8. Thesystem of claim 6, wherein the first trade instructions and the secondtrade instructions are instructions for a statistical arbitrage trade.9. The system of claim 6, wherein the first trade instructions and thesecond trade instructions are instructions for a pairs trade.
 10. Thesystem of claim 6, wherein the server coupled to the communication linkat the identified physical location is further configured to send signedfirst trade instructions and signed second trade instructions to thefirst trading center.
 11. A method for identifying a physical locationalong a communication link between a first trading center and a secondtrading center at which to couple to the communication link a server forsending trading instructions to the first trading center and/or thesecond trading center, the method comprising: obtaining a property ofthe communication link; and identifying the physical location at whichto physically couple the server to the communication link, wherein theidentifying comprises calculating, with at least one processor, alocation based at least in part on the obtained property of thecommunication link and at least one characteristic of a first financialinstrument traded at the first trading center, wherein the at least onecharacteristic of the first financial instrument includes a rate atwhich a value depending on a price of the first financial instrumentmoves to its long term trend over a predetermined period of time. 12.The method of claim 11, further comprising: connecting the server to thecommunication link at or near the calculated location.
 13. The method ofclaim 11, wherein calculating the location for the server furthercomprises calculating the location based on the at least onecharacteristic of the first financial instrument traded at the firsttrading center and at least one characteristic of a second financialinstrument traded at the second trading center.
 14. The method of claim13, wherein calculating the location comprises weighting a valueindicative of the property of the communication link by a value derivedfrom the at least one characteristic of the first financial instrumentand the at least one characteristic of the second financial instrument.15. The method of claim 11, wherein the first trading center is anexchange or an over-the-counter market.
 16. The method of claim 11,wherein the communication link comprises fiber-optic cable and theproperty of the communication link is a latency of propagation of lightthrough the fiber-optic cable.
 17. At least one non-transitorycomputer-readable storage medium encoded with processor-executableinstructions that, when executed by at least one processor, cause the atleast one processor to perform a method for identifying a physicallocation along a communication link between a first trading center and asecond trading center at which to couple to the communication link aserver for sending trading instructions to the first trading centerand/or the second trading center, the method comprising: obtaining aproperty of the communication link; and identifying the physicallocation at which to physically couple the server to the communicationlink, wherein the identifying comprises calculating a location based atleast in part on the obtained property of the communication link and atleast one a characteristic of a first financial instrument traded at thefirst trading center, wherein the at least one characteristic of thefirst financial instrument includes a rate at which a value depending ona price of the first financial instrument moves to its long term trendover a predetermined period of time.
 18. The at least one non-transitorycomputer-readable storage medium of claim 17, wherein the method furthercomprises calculating the location based at least in part on the atleast one characteristic of the first financial instrument and at leastone characteristic of a second financial instrument traded at the secondtrading center.
 19. The at least one non-transitory computer-readablestorage medium of claim 18, wherein: the first financial instrument isan equity traded at the first trading center and at least anothertrading center; and the at least one characteristic of the firstfinancial instrument includes a value depending on a price of theequity.